Moreover, observations indicate that the possibility of a mutual
interaction between the DM and DE, which may solve the coincidence
problem, is not zero [1]}. The simplest form of this
mutual interaction can be written as \(Q=3b^2H\rho \)  in which \(b^2\) 
is a constant and \(\rho \)  can be the energy density of DM, DE or
even their sum [1]}. Since \(b^2\)  is constant and \(H\) 
and \(\rho \)  are positive quantities, the sign of the interaction
term is not changed during the cosmic evolution. However, recent
investigations confirm that the sign of the interaction between DM
and DE is changed during the history of the universe and in
particular in the redshift \(0\cdot 45\le z\le 0\cdot 9\) 
[3]}. Clearly, the sign-changeable interaction term
cannot be described by the \(Q=3b^2H\rho \)  expression. Following
[3]}, Wei proposed the sign-changeable interaction term
as \(Q=q(\alpha \dot{\rho }+3\beta H{\rho })\)  for the mutual
interaction [5]}, [6]}. In this new expression, both
\(\alpha \)  and \(\beta \)  are dimensionless constant and
\(q=-1-\dot{H}/H^2\)  is the deceleration parameter. The key
ingredient is the deceleration parameter \(q\)  in the interaction
\(Q\) , and hence the interaction \(Q\)  can change its sign when our
universe changes from deceleration phase \((q > 0)\)  to acceleration
\((q < 0)\) . The \(\alpha \dot{\rho }\)  and \(\beta H{\rho }\)  terms are
introduced from the dimensional point of view
[5]}, [8]}, [9]}, and one can ignore the
\(\alpha \dot{\rho }\)  term by considering \(\alpha =0\) 
[5]}, [8]}, [9]}. It is worth noting that the
\(Q(\rho ,\dot{\rho })\)  form has previously been introduced to
describe the mutual interaction between the dark sectors of cosmos
[8]}, [9]}. Now, bearing the Firedmann equation in
mind (\(H^2\propto \rho \) ), we find out that the \(Q(\rho ,\dot{\rho })\) 
interaction can indeed be written in the \(Q(H,\dot{H})\)  form. On
the other hand, since \(q=q(H,\dot{H})\) , the \(Q=q(\alpha \dot{\rho }+3\beta H{\rho })\)  interaction can also be written in the
form \(Q(H,\dot{H})\) , meaning that in the Wei's approach, the
appearance of the deceleration parameter, \(q\) , in the interaction
term \(Q\)  is quite acceptable [5]}, [6]}.
